Density of debris fragments through differential algebra and averaged dynamics

The modeling of space debris objects is a difficult task. In this work Differential Algebra (DA) techniques are coupled with semi-analytical averaged dynamics to describe the density evolution of debris fragments in the space of orbital elements. Given an initial probability density function, DA is used to propagate the probability density function to any given time by means of a high order polynomial expansion. The effect of orbit perturbations is described through averaged dynamics. We use the proposed DA+average dynamics approach to represent the time evolution of a cloud of debris fragments in Medium Earth Orbit and their density in time. This allows to assess the consequent risk of intersection between the cloud of resulting orbit and a target orbit.